Assertion (A) : 155 × 277 + 155 × (-45) = 155 × [277 + (-45)]
Reason (R) : Distributive property holds for any three integers. i.e. a × (b + c) = a × b + a × c, for all integers a, b, c.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A) is the distributive property applied to 155, 277 and (-45), so it is true.
Reason (R) correctly states the distributive property, which holds for all integers, so it is true. Also, R is the correct explanation of A.
So, both A and R are true.
Hence, option 3 is the correct option.
Assertion (A) : (-59) × (-47) ≠ (47) × (59)
Reason (R) : For any integers a and b, a × b = b × a
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A) : (-59) × (-47) = 59 × 47 = 2773 and (47) × (59) = 2773. Since both are equal, the statement (-59) × (-47) ≠ (47) × (59) is false. So A is false.
Reason (R) : Multiplication of integers is commutative, i.e. a × b = b × a. So R is true.
So, A is false and R is true.
Hence, option 2 is the correct option.
Assertion (A) : The product of two integers is -775. If one of them is 25, the other integer is 31.
Reason (R) : If a and b are two integers, then a ÷ b or b ÷ a may or may not be an integer.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
Assertion (A) : The other integer = (-775) ÷ 25 = -31, not 31. So A is false.
Reason (R) : For two integers a and b, the quotient a ÷ b or b ÷ a may or may not be an integer. So R is true.
So, A is false and R is true.
Hence, option 2 is the correct option.